Compressive failure of fiber composites under multi-axial loading

This paper examines the compressive strength of a fiber reinforced lamina under multi-axial stress states. An equilibrium analysis is carried out in which a kinked band of rotated fibers, described by two angles, is sandwiched between two regions in which the fibers are nominally straight. Proportional multi-axial stress states are examined. The analysis includes the possibility of bifurcation from the current equilibrium state. The compressive strength of the lamina is contingent upon either attaining a load maximum in the equilibrium response or satisfaction of a bifurcation condition, whichever occurs first. The results show that for uniaxial loading a non-zero kink band angle β produces the minimum limit load. For multi-axial loading, different proportional loading paths show regimes of bifurcation dominated and limit load dominated behavior. The present results are able to capture the beneficial effect of transverse compression in raising the composite compressive strength as observed in experiments.     

Multiscale modeling of strain-hardening cementitious composites

This research involves the multiscale characterization of strain-hardening cementitious composites under tensile loading. The sensitivity of cracking behavior to fiber dispersion is studied using a special form of lattice model, in which each fiber is explicitly represented. It is shown that the nonlocal modeling of fiber bridging forces is essential for obtaining realistic patterns of crack development and strain-hardening behavior. Crack count and crack size are simulated for progressively larger levels of tensile strain. The influence of fiber dispersion is clearly evident: regions with significantly fewer fibers act as defects, reducing strength and strain capacity of the material.     

Rheological characterization of continuous fiber—reinforced viscous fluid

The present paper describes a micromechanical technique to determine rheological properties of viscous fluid reinforced with unidirectional continuous fibers. Fluid viscosity is described by a shear thinning model and high viscosity is considered for continuous fibers having considerable rigidity compared to net fluid. The microstructure is identified by a representative volume element that is subjected to equivalent macroscopic deformation fields. The energy balance and periodicity conditions are considered to relate deformation and stress in macro and micro-levels. It is shown that response of viscous fluid reinforced with rigid fibers depends on deformation history as well as rate-of-deformation in the transverse intraply shear and transverse squeeze flows. An orthotropic viscous constitutive equation is derived to describe response of such materials. The material viscosities are evaluated for viscous fluid reinforced with different fiber volume fractions during deformation applied in different rates of deformation. The results are used to derive the functions predicting effective anisotropic viscosities of reinforced fluid.     

Torsional Swelling of a Hyperelastic Tube with Helically Wound Reinforcement

This paper examines the combination of radial deformation with torsion for a circular cylindrical tube composed of a transversely isotropic hyperelastic material subject to finite deformation swelling. The stored energy function involves separate matrix and fiber contributions such that the fiber contribution is minimized when the fiber direction is at a natural length. This natural length is not affected by the swelling. Hence swelling preferentially expands directions that are orthogonal to the fiber. The swelling itself is described via a swelling field that prescribes the local free volume at each location in the body. Such a treatment is a relatively simple generalization of the conventional incompressible theory. The direction of transverse isotropy associated with the fiber reinforcement is described by a helical winding about the tube axis. The swelling induced preferential expansion orthogonal to this direction induces the torsional aspect of the deformation. For a specific class of strain energy functions we find that the twist increases with swelling and approaches a limiting asymptotic value as the swelling becomes large. The fibers reorient such that fibers at the inner portion of the tube assume a more circumferential orientation whereas, at least for small and moderate swelling, the fibers in the outer portion of the tube assume a more axial orientation. For large swelling the fibers in the outer portion of the tube reorient beyond the axial orientation, and so are described by helices with orientation in the opposite sense to that in the reference configuration.      

A homogenization theory for time-dependentnonlinear composites with periodic internal structures

A homogenization theory for time-dependent deformation such as creep andviscoplasticity of nonlinear composites with periodic internal structures is developed. To beginwith, in the macroscopically uniform case, a rate-type macroscopic constitutive relation betweenstress and strain and an evolution equation of microscopic stress are derived by introducing twokinds of Y-periodic functions, which are determined by solving two unit cell problems.Then, the macroscopically nonuniform case is discussed in an incremental form using thetwo-scale asymptotic expansion of field variables. The resulting equations are shown to beeffective for computing incrementally the time-dependent deformation for which the history ofeither macroscopic stress or macroscopic strain is prescribed. As an application of the theory,transverse creep of metal matrix composites reinforced undirectionally with continuous fibers isanalyzed numerically to discuss the effect of fiber arrays on the anisotropy in such creep.     

Analysis of a high intensity shear zone between overlapping fiber ends in a polymer matrix composite

The formation of high intensity shear zones in a glass fiber reinforced thermoplast is studied numerically. The thermoplast is characterized by a finite strain elastic-viscoplastic constitutive relation and the calculations are carried out using a dynamic finite element program where plane strain conditions are assumed to prevail in the direction of the thickness. Different ratios of the elongation strain and the transverse strain are studied to consider the effect of different levels of stress triaxiality and the effect of these states on the shear zone development and emerging strain and stress concentrations. Comparing a case of embedded infinitely stiff fibers to a case with glass fiber reinforcement shows little difference thus illustrating that the glass fibers act approximately as infinitely stiff. Fiber spacing and fiber width are shown to influence the shear zones and the stress fields that develop as the highly deformed region approaches the limit resulting from network stiffening in the polymer. A simple analysis assuming periodicity is included in order to study the mechanical behaviour of the polymer matrix between fiber ends with long overlap.     

A structural multi-mechanism constitutive equation for cerebral arterial tissue

A structural multi-mechanism constitutive equation is developed to describe the nonlinear, anisotropic, inelastic mechanical behavior of cerebral arterial tissue. Elastin and collagen fibers are treated as separate components (mechanisms) of the artery. Elastin is responsible for load bearing at low strain levels while the collagen mechanism is recruited for load bearing at higher strain levels. This work builds on an earlier model in which both the elastin and collagen mechanisms are represented by isotropic response functions [Wulandana, R., Robertson, A.M., 2005. An inelastic multi-mechanism constitutive equation for cerebral arterial tissue. Biomech. Model. Mechan. 4 (4), 235–248]. Here, the anisotropic material response of the wall is introduced through the collagen mechanism which is composed of helically distributed families of fibers. The orientation of these families is described using either a finite number of fiber orientations or a fiber distribution function. The fiber orientation or dispersion function can be prescribed directly from arterial histology data, or, taking a phenomenological approach, based on data fitting from bi-axial measurements. The activation of the collagen mechanism is specified using a new fiber strain based activation criterion. The multi-mechanism constitutive equation is applied to the simple case of cylindrical inflation and material constants are determined based on available inelastic experimental data for cerebral arteries. While the proposed model captures all features of this inelastic data, there is a pressing need for further experiments to refine the model.     

On the transverse compression response of Kevlar KM2 using fiber-level finite element model

Flexible textile composites like woven Kevlar fabrics are widely used in high velocity impact (HVI) applications. Upon HVI they are subjected to both longitudinal tensile and transverse compressive loads. To understand the role of transverse properties, the single fiber and tow transverse compression response (SFTCR and TTCR) of Kevlar KM2 fibers are numerically analyzed using plane strain finite element (FE) models. A finite strain formulation with a minimum number of 84 finite elements is determined to be required for the fiber cross section to capture the finite strain SFTCR through a mesh convergence study. Comparison of converged numerical solution to the experimental results indicates the dominant role of geometric stiffening at finite strains due to growth in contact width. The TTCR is studied using a fiber length scale FE model of a single tow comprised of 400 fibers transversely loaded between rigid platens. This study along with micrographs of yarn after mechanical compaction illustrates fiber spreading and fiber–fiber contact friction interactions are important deformation mechanisms at finite strains. The TTCR is also studied using homogenized yarn level models with properties from the literature. Comparison of TTCR between fiber length scale and homogenized yarn length scale models indicate the need for a nonlinear material model for homogenized approaches to accurately predict the transverse compression response of the fabrics.     

A periodic unit-cell simulation of fiber arrangement dependence on the transverse tensile failure in unidirectional carbon fiber reinforced composites

The effect of fiber arrangement on transverse tensile failure in unidirectional carbon fiber reinforced composites with a strong fiber-matrix interface was studied using a unit-cell model that includes a continuum damage mechanics model. The simulated results indicated that tensile strength is lower when neighboring fibers are arrayed parallel to the loading direction than with other fiber arrangements. A shear band occurs between neighboring fibers, and the damage in the matrix propagates around the shear band when the interfacial normal stress (INS) is sufficiently high. Moreover, based on the observation of Hobbiebrunken et al., we reproduced the damage process in actual composites with a nonuniform fiber arrangement. The simulated results clarified that the region where neighboring fibers are arrayed parallel to the loading direction becomes the origin of the transverse failure in the composites. The cracking sites observed in the simulation are consistent with experimental results. Therefore, the matrix damage in the region where the fiber is arrayed parallel to the loading direction is a key factor in understanding transverse failure in unidirectional carbon fiber reinforced composites with a strong fiber/matrix interface.     

Some exact plane elasticity solutions for nonhomogeneous,orthotropic sheets

Exact plane stress solutions are presented for composite material sheets made of parallel fibers embedded in matrix materials. The fibers have variable spacing, and the resulting material is macroscopically orthotropic and nonhomogeneous. Formulas for the variable elastic coefficients are presented for arbitrary fiber spacing. Exact solutions for the stress, strain and displacement fields are presented for four types of problems with arbitrary fiber spacing: (1) Uniform normal stress on the edges parallel to the fibers (i.e., the longitudinal edges), zero normal displacement on the transverse edges; (2) zero normal stress on the longitudinal edges, uniform normal displacement on the transverse edges; (3) zero normal displacement in the longitudinal edges, uniform normal displacement on the transverse edges; and (4) zero normal displacement on the longitudinal edges, uniform shear stress on all edges. For the first three problems, the shear stresses on all boundaries are zero. For the last one, the normal stress on the transverse edge is zero.     

Influence of fiber’s shape and size on overall elastoplastic property for micropolar composites

A general micromechanical method is developed for a micropolar composite with ellipsoidal fibers, where the matrix material is idealized as a micropolar material model. The method is based on a special micro–macro transition method, and the classical effective moduli for micropolar composites can be determined in an analytical way. The influence of both fiber’s shape and size can be analyzed by the proposed method. The effective moduli, initial yield surface and effective nonlinear stress and strain relation for a micropolar composite reinforced by ellipsoidal fibers are examined, it is found that the prediction on the effective moduli and effective nonlinear stress and strain curves are always higher than those based on classical Cauchy material model, especially for the case where the size of fiber approaches to the characteristic length of matrix material. As expected, when the size of fiber is sufficiently large, the classical results (size-independence) can be recovered.     

Mircopolar Model of Fracture for Composite Material

Failure of a composite is a complex process accompanied by irreversible changes in the microstructure of the material. Microscopic mechanisms are known of the accumulation of damage and failure of the type of localized and multiple ruptures of the fibers delamination along interphase boundaries, and also mechanisms associated with fracture of fibers. In this work, we propose a mathematical model of the local mechanism of failure of a composite material randomly reinforced with a system of short fibers. We implement the Cosserat moment model of crack tip for filament material, reinforced with whiskers or in fiber- reinforced polycrystalline materials. It is assumed that the angular distribution of the fibers is isotropic and the elastic characteristics of the fibers are considerably higher than the elastic constants of the matrix. We implement the homogenization procedure for the effective Cosserat constants similarly to the effective elastic constants. The singular solution in the vicinity of the crack tip in the Cosserat moment model is found. Using this solution, we examine the bending stresses in the filaments due to effective moment stresses in the material. The constructed model describes the phenomenon of fracture of the fibers occurring during crack propagation in those composites. The following assumptions are used as the main hypotheses for the micromechanical model. The matrix contains a nucleation crack. When the load is increased the crack grows and its boundary comes into contact with the reinforcing fibers. A further increase of the stress causes bending of the fiber. When~the fiber curvature reaches a specific critical value, the fiber ruptures. If the stress at infinity is given, the fibers no longer delay the development of failure during crack propagation The degree of bending distortion of the fiber in the vicinity of the boundary of the crack is determined by the moment model of the material. The necessity to take into account the moment stresses in the failure theory of the reinforced material was stressed in [Muki and Sternberg (1965) Zeitschrift f angew Math und Phys 16:611–615; Garajeu and Soos (2003) Math Mech Solids 8(2):189–218; Ostoja-Starzewski et al (1999) Mech Res Commun 26:387–396]. The moment Cosserat stresses were accounted also for inhomogeneous biomechanical materials by Buechner and Lakes (2003) Bio Mech Model Mechanobiol 1: 295–301. We should also mention the important methodological studies [Sternberg and Muki (1967) J Solids Struct 1:69–95; Atkinson and Leppington (1977) Int J Solids Struct 13: 1103–1122] concerned with the moment stresses in homogeneous fracture mechanics.     

A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids

We consider an incompressible nonlinearly elastic material in which a matrix is reinforced by strong fibers, for example fibers of nylon or carbon aligned in one family of curves in a rubber matrix. Rather than adopting the constraint of fiber inextensibility as has been previously assumed in the literature, here we develop a theory of fiber-reinforced materials based on the less restrictive idea of limiting fiber extensibility. The motivation for such an approach is provided by recent research on limiting chain extensibility models for rubber. Thus the basic idea of the present paper is simple: we adapt the limiting chain extensibility concept to limiting fiber extensibility so that the usual inextensibility constraint traditionally used is replaced by a unilateral constraint. We use a strain-energy density composed with two terms, the first being associated with the isotropic matrix or base material and the second reflecting the transversely isotropic character of the material due to the uniaxial reinforcement introduced by the fibers. We consider a base neo-Hookean model plus a special term that takes into account the limiting extensibility in the fiber direction. Thus our model introduces an additional parameter, namely that associated with limiting extensibility in the fiber direction, over previously investigated models. The aim of this paper is to investigate the mathematical and mechanical feasibility of this new model and to examine the role played by the extensibility parameter. We examine the response of the proposed models in some basic homogeneous deformations and compare this response to those of standard models for fiber reinforced rubber materials. The role of the strain-stiffening of the fibers in the new models is examined. The enhanced stability of the new models is then illustrated by investigation of cavitation instabilities. One of the motivations for the work is to apply the model to the biomechanics of soft tissues and the potential merits of the proposed models for this purpose are briefly discussed.     

Rheological behavior of fiber-filled polymers under large amplitude oscillatory shear flow

Small and large amplitude oscillatory shear measurements (SAOS and LAOS) were used to investigate the rheological behavior of short glass fibers suspended in polybutene and molten polypropylene. Raw torque and normal force signals obtained from a strain-controlled instrument (ARES rheometer) were digitized using an analog to digital converter (ADC) card to allow more precise data analysis. The fiber concentration did not affect the torque signal in the SAOS mode, except for its magnitude, whereas the normal force signal was too low to be measurable. With increasing strain amplitude, the magnitude of the torque became a function of time. Depending on the applied frequency and strain rate, the stress in the filled polybutene increased with time, whereas for reinforced polypropylene (viscoelastic matrix), the behavior was opposite, i.e. the stress decreased with time. These effects were more pronounced at high fiber content. In addition the primary normal stress differences were no longer negligible at large deformation amplitude and exhibited a non-sinusoidal periodic response. Fast Fourier transform (FFT) analysis was performed and the resulting spectra, along with Lissajous figures of the shear stress and the primary normal stress differences, are explained in terms of fiber orientation. The experimental results for the suspensions in polybutene are well predicted by the Folgar-Tucker-Lipscomb (FTL) model.     

Two-dimensional buckling problem for a composite reinforced with a periodic row of collinear short fibers

A solution is found to the two-dimensional buckling problem for a composite material reinforced with a periodic row of collinear short fibers and compressed along the fibers. The problem formulation is based on the piecewise-homogeneous model and the three-dimensional theory of stability of deformable bodies. The dependence of the critical strain and buckling mode on the fiber spacing is studied for various material and geometrical characteristics of the composite components __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 90–100, June 2006.     

Prediction of thermal conductivity of air voided-fiber-reinforced composite laminates part II: 3D simulation

Applying the fundamental definition of thermal conductivity to a unit cell of unidirectional fiber reinforced composite with air voids, one can deduce simple empirical formula to predict the thermal conductivity of the composite material with estimated air void volume percent. The inherent 3-D problem is modeled using finite element analysis. The model is tested at different fiber to resin volume ratios and various fibers to resin thermal conductivity ratios for three different air void volume percent. The air voids are modeled as cylindrical shapes with different lengths aligned with fiber direction. Two prediction schemes have been developed through the present work. One is to predict the longitudinal thermal conductivity and the other is to predict the transverse thermal conductivity of the fibers. Also, the model can be used to estimate the voids volume percent if the fiber thermal conductivity has been provided. Such expression can, also, serve as useful guides for quality and perfect bonding for material development.     

A simple estimate for the effect of cross sensitivity on evaluated strain-gage measurement

The cross-sensitivity factor of a short-wire strain gage can sometimes be estimated by comparison of its gage factor with that of a long gage of similar construction and material. A plot of the error introduced by the usual neglect of cross sensitivity against the known or estimatedtrue ratio of transverse to longitudinal stress or strain yields a quick estimate for any given cross-sensitivity factorn of the gage, any Poisson's ratio ν of the test piece and any stress or strain ratio. It shows whether in any particular test the influence of cross sensitivity warrants further special attention. If the longitudinal strain exceeds the transverse strain, the error is seen to be always less than 1.3n, but if the transverse strain is larger, the error may be so high as to vitiate the result. In computations from rosette measurements, the diagram shows that the larger principal stress can be determined with an error below 1.3n, as can Tresca's and von Mises's criteria of yield, while the error in the smaller principal stress tends to be large for principal strain ratios above +10 or below ?1.5.     

增强纤维对陶瓷基摩擦材料摩擦磨损性能的影响

采用热压烧结法制备纤维增强陶瓷基摩擦材料,研究了钢纤维、钢纤维/莫来石纤维、莫来石纤维、钢纤维/硅酸铝纤维以及硅酸铝纤维增强陶瓷基摩擦材料的摩擦磨损特性.研究结果表明:不同纤维对陶瓷基摩擦材料摩擦系数的影响较为复杂.相比较添加单一纤维增强摩擦材料的情况,钢纤维增强的试样具有较好的耐磨性能,其次为莫来石纤维增强的试样,硅酸铝纤维增强的试样表现出最差的耐磨性能,钢纤维/莫来石纤维和钢纤维/硅酸铝纤维增强试样的磨损均低于相应的陶瓷纤维增强的试样;在高温下以莫来石纤维增强的试样,其磨损形式以磨粒磨损为主,而以硅酸铝纤维和钢纤维/硅酸铝纤维增强的试样的主要磨损形式为黏着磨损,钢纤维和钢纤维/莫来石纤维增强的试样的磨损属于磨粒磨损和黏着磨损.     

Numerical prediction of fiber motion in a branching channel flow of fiber suspensions

Fiber orientation and dispersion in the dilute fiber suspension that flows through a T-shaped branching channel are simulated numerically based on the slender-body theory. The simulated results are consistent qualitatively with the experimental data available in the literature. The results show that the spatial distribution of fibers is dependent on the fiber aspect ratio, but has no relation with the volume fraction of fiber. The content ratio of fibers near the upper wall increases monotonically with an increasing Re number, and the situation is reverse for the region near the bottom wall. The orientation of fibers depends on Re number, however, the function of fiber volume fraction and aspect ratio is negligible. The fibers near the wall and in the central region of the channel align along the flow direction at all times, but the fibers in the other parts of the channel tend to align along the flow direction only in the downstream region.The project supported by the National Natural Science Foundation of China (10372090) and Doctoral Program of Higher Education in China (20030335001)The English text was polished by Ron Marshall